New perspective on the optical theorem of classical electrodynamics

A proof of the optical theorem (also known as the optical cross-section theorem) is presented, which reveals the intimate connection between the forward scattering amplitude and the absorption-plus-scattering of the incident wave within the scatterer. The oscillating charges and currents as well as the electric and magnetic dipoles of the scatterer, driven by an incident plane wave, extract energy from the incident beam. The same oscillators radiate electromagnetic energy into the far field, thus giving rise to well-defined scattering amplitudes along various directions. The essence of the proof presented here is that the extinction cross-section of an object can be related to its forward scattering amplitude using the induced oscillations within the object without knowledge of the form assumed by these oscillations.